Non-linear electromagnetic interactions in thermal QED

We examine the behavior of the non-linear interactions between electromagnetic fields at high temperature. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T tends to infinity. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.